Asymptotic behavior of exotic Lagrangian tori Ta,b,c in CP2 as a plus b plus c → ∞

被引：0

作者：

Lee, Weonmo ^{[1
,2
]}

Oh, Yong-Geun ^{[1
,2
]}

Vianna, Renato ^{[3
]}

机构：

[1] POSTECH, Dept Math, Pohang 37673, South Korea

[2] IBS Ctr Geometry & Phys, Pohang 37673, South Korea

[3] Univ Fed Rio de Janeiro, Inst Math, BR-21941909 Rio De Janeiro, Brazil

来源：

JOURNAL OF SYMPLECTIC GEOMETRY | 2021年 / 19卷 / 03期

关键词：

SYMPLECTIC TOPOLOGY; FLOER COHOMOLOGY; GROMOV WIDTH; SUBMANIFOLDS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori T-a,T-b,T-c in CP2 associated to Markov triples (a, b, c) described in [Via16]. We first prove that the Gromov capacity of the complement CP2\T-a,T-b,T-c is greater than or equal to 1/3 of the area of the complex line for all Markov triple (a, b, c). We then prove that there is a representative of the family {T-a,T-b,T-c} whose loci completely miss a metric ball of nonzero size and in particular the loci of the union of the family is not dense in CP2.

引用

页码：607 / 634

页数：28

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